As you would be changing the crank and chain rings only, the Sora front derailleur should work with the 105 assembly. Crank length would need to suit the rider.
You haven't stated how many gears are on the cluster. You must consider that the 8 & 9 speed chain and spacing is different to the 10 speed chain and spacing. If you are not changing the spacing of the chain rings then this would mean that the existing front derailleur should be adequate.
sora takes a 27 rear cassette but some frames may be able to stretch to a larger one. may need a longer chain or to add spare links left over from your last new chain.
Or get a mtb rear derailleur and cassette
Buy another bike with compact or a triple, swap parts then resell it?
Chain Reaction have a sora compact 34T chain ring for $20 + postage. This could be a simple and cheap solution
I'm guessing you're not a Shimano man Dave. 11 speed Dura Ace, Ultegra and 105 are all now one BCD.
May be cheaper to get a bigger cassette and a long-cage rear derailleur. How many speed is it? 39/32 will be a big difference from 39/25. Of course 34/32 would be ideal.
Yes compact cranks have a smaller BCD (bolt circle diameter) so you can't simply swap over to a smaller chainring.
I agree with Tom, new cassette, rear derailleur and chain. Cheapest option and biggest range of gears. About $75 including delivery if you buy online. This assumes you have the tools & knowledge to swap over.
You could try the Adelaide Community Bicycle Workshop. They may be able to sell you the necessary parts second hand for a lot less and help/teach you to install them using their tools.
If it is an 8 speed then dropping down from the 3xxx "Sora" range to a 2300 rear derailleur would be a good start as this is compatible with 3 chain rings with a difference of 22T and cluster ranges 26/13 maximum and 21/12 minimum.
The bolt circle is also called a spider even though they always have 5/4 and not 8 legs.